Rough volatility models using the signature transform: theory and calibration

Abstract

[en] In this thesis we study a general stochastic volatility model where the dynamics of the volatility process are described by using the signature transform, a key object in rough path theory which is also very popular in the machine learning community due to its fundamental properties in approximation theory. More specifically, we will present a general model for the evolution of the price of the underlying asset where the dynamics of the volatility are described by linear functions of the (time extended) signature of a primary underlying process. We will finally use this model in practice, showing how it can be efficiently calibrated to market prices of options by a Monte Carlo simulation.